Page 191 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 12 : Linear Regression Analysis : Introduction and Lines of Regression

• The word regression, which means reversion, was first introduced by Sir Francis Galton in the Notes
study of heredity. His study on the heights of fathers and sons revealed an interested relationship. He
showed that the heights of sons tended or reverted towards the average rather than two extreme values,
i.e., tall fathers tend to have tall sons and short fathers short sons, but the average height of the sons of a
group of short fathers is greater than that of fathers. Galton termed the line describing the average
relationship between the two variables as the line of regression. Thus, by regression we mean the average
relationship between two or more variables which can be used for estimating the value of one variable
from the given values of one or more variables.
• Under correlation, the direction and magnitude of the relationship between two variables is
measured. But it is not possible to make the best estimate of the value of a dependent variable
on the basis of the given value of the independent variable by correlation analysis. Therefore,
to make the best estimates and future estimation, the study of regression analysis is very
important and useful.
• In statistical analysis, the term ‘Regression’ is taken in wider sense. Regression is the study of
the nature of relationship between the variables so that one may be able to predict the
unknown value of one variable for a known value of another variable. In regression, one
variable is considered as an independent variable and another variable is taken as dependent
variable. With the help of regression, possible values of the dependent variable are estimated
on the basis of the values of the independent variable. For example, there exists a functional
relationship between demand and price, i.e., D = f (P). Here, demand (D) is a dependent variable,
and price (P) is an independent variable. On the basis of this relationship between demand and
price, probable values of demand can be estimated corresponding to the different values of
price.
• By regression analysis, the value of a dependent variable can be predicated on the basis of the
value of an independent variable. For example, if price of a commodity rises, what will be the
probable fall in demand, this can be predicted by regression.
• If the variables in a bivariate frequency distribution are correlated, we observe that the points
in a scatter diagram cluster around a straight line called the line of regression.
• The line of regression of X and Y is used to estimate or predict the value of X for a given value of the
variable Y. In this case X is the dependent variable and Y is the independent variable.
12.4 Key-Words

1. Linear Regression Analysis : In statistics, regression analysis is a statistical technique for
estimating the relationships among variables. It includes many
techniques for modeling and analyzing several variables, when
the focus is on the relationship between a dependent variable and
one or more independent variables. More specifically, regression
analysis helps one understand how the typical value of the
dependent variable changes when any one of the independent
variables is varied, while the other independent variables are held
fixed. Most commonly, regression analysis estimates the
conditional expectation of the dependent variable given the
independent variables - that is, the average value of the dependent
variable when the independent variables are fixed. Less commonly,
the focus is on a quantile, or other location parameter of the
conditional distribution of the dependent variable given the
independent variables. In all cases, the estimation target is a
function of the independent variables called the regression
function. In regression analysis, it is also of interest to characterize
the variation of the dependent variable around the regression
function, which can be described by a probability distribution.

LOVELY PROFESSIONAL UNIVERSITY 185